The manager named a 20-man squad for the trip to Italy on Monday, with the Reds jetting out in the afternoon before finalising preparations at the Stadio San Paolo in the evening.
Origi, who suffered a knock against Newcastle at the weekend, was excluded from the squad, with Liverpool youngster Rhian Brewster taking his place.
“The update on Div is that it is not too serious,” Klopp told the club website.
“We expect him [to be out for] between one and two weeks, but it depends a little bit on when he can deal with the pain.
“It is nothing really; it's a feeling, but it should be fine.”
Meanwhile, Robertson didn't train with the rest of the squad at Melwood on Monday morning, with Klopp still unsure whether the Scotsman will start.
“Robbo didn't train today and we have to see. It is not a major thing, it was more precautionary today, but it is not 100 per cent sure [that he will be available].
“We will have to test it tomorrow and then we will see.”
Robertson, alongside fellow full-back Trent Alexander-Arnold, is a crucial player for Jurgen Klopp's side and he would be a huge miss should he fail to make the starting eleven.